### Abstract

We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

Original language | English |
---|---|

Pages (from-to) | 873-907 |

Number of pages | 35 |

Journal | Progress of Theoretical Physics |

Volume | 115 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Progress of Theoretical Physics*,

*115*(5), 873-907. https://doi.org/10.1143/PTP.115.873

**Adiabatic evolution of orbital parameters in Kerr spacetime.** / Sago, Norichika; Tanaka, Takahiro; Hikida, Wataru; Ganz, Katsuhiko; Nakano, Hiroyuki.

Research output: Contribution to journal › Article

*Progress of Theoretical Physics*, vol. 115, no. 5, pp. 873-907. https://doi.org/10.1143/PTP.115.873

}

TY - JOUR

T1 - Adiabatic evolution of orbital parameters in Kerr spacetime

AU - Sago, Norichika

AU - Tanaka, Takahiro

AU - Hikida, Wataru

AU - Ganz, Katsuhiko

AU - Nakano, Hiroyuki

PY - 2006/5/1

Y1 - 2006/5/1

N2 - We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

AB - We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

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U2 - 10.1143/PTP.115.873

DO - 10.1143/PTP.115.873

M3 - Article

AN - SCOPUS:33747737961

VL - 115

SP - 873

EP - 907

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -